Following Immigration Minister Scott Morrison's visit to India, the Indian High Commission in Canberra has told the ABC Indian officials want to establish who they are and where they set sail from.

The High Commission's first secretary Tarun Kumar would not elaborate on why his government is seeking the information.

However, Mr Kumar emphasised the importance of handling the matter "in a legal and humanitarian" way, ensuring the asylum seekers come to no harm.

Lawyers for the Sri Lankan asylum seekers held on board an Australian Customs ship are seeking a court order preventing the Federal Government from sending them to Sri Lanka, Nauru or Papua New Guinea.

Instead, the group wants to be sent to Australia or another country that "has assumed the international law non-refoulement obligations".

In its defence statement filed to the court yesterday, the Federal Government said the people on board the vessel did not hold visas entitling them to travel or to enter Australia.

Justice Hayne told yesterday's hearing he was not happy with the plaintiff's draft case and labelled the Government's defence as ambiguous and lax.

He also expressed concern about the length of time the asylum seekers had been on the ship.

The asylum seekers were transferred to a Customs ship, thought to be ACV Ocean Protector, about three weeks ago.

It was previously believed 153 people were on board.

They will remain at sea until the end of the case, meaning they could be at sea for a few more weeks.

The Human Rights Law Centre's Hugh de Kretser says he hopes the court can make a decision as soon as possible.

"We hope that the court after that two-day hearing will make that decision very quickly, bearing in mind that every day that this case proceeds is another day that 157 people are kept on board a vessel detained somewhere on the high seas," Mr de Kretser said.

Lawyers for the asylum seekers say their clients are being held against their will "behind locked doors" without "freedom of movement" and that families on the ship have been split up.

Immigration Minister Scott Morrison has told Parliament the asylum seekers are in good care.

"Any person who is in the care and protection of the Australian Customs and Border Protection Service will be in good care, and they are in good care," he said.